Cross Z-Complementary Sets for Training Design in Spatial Modulation

Spatial modulation (SM) is one special type of multiple-input multiple-output (MIMO) technique whose advantage is that only one radio-frequency (RF) chain is needed. Recently, the so-called cross Z-complementary pair (CZCP) was proposed as the SM training sequence. Optimal channel estimation performance over frequency-selective channels can be achieved since the CZCPs have the specific zero correlation zone (ZCZ) for auto-correlation and cross-correlation sums. However, the ZCZ width of the CZCP is theoretically upper bounded by half sequence length. In this paper, the CZCP is extended to the cross Z-complementary set (CZCS) to have larger ZCZ width which can be used in SM to combat larger delay spread. Several generic constructions of CZCSs with large ZCZ widths and flexible lengths are proposed in this paper. Even the perfect CZCS, whose ZCZ width has the maximum value, can be obtained. Numerical simulations demonstrate that the proposed CZCS-based training sequence can tolerate large delay spreads to improve the channel estimation performance in SM.